The warming is large: In the last 40 years the upper 700 meters of the Atlantic Ocean have gained heat at a rate of 20 ZJ/decade. (Here "Z" = "zetta" = 1021, which I used only because I've never had the chance to use it before.)
|The Agulhas Current around south Africa|
These are large amounts. For the Atlantic Ocean it works out to 60 TW (terawatts; tera = 1012), which is 4 times the amount of energy used by humans worldwide.
Put another way, though, it's only 0.04% of incident solar energy. (The latter value is 170 PW (petawatts), where "peta" = 1015.)
Why have these oceans warmed? You get one guess (hint: it's a three-letter word, and rhymes with "can."). Click here for the answer.
But why has the Atlantic warmed more than the Pacific or the Indian, when it comprises only 20% of oceanic surface area? That's more complicated, and I can't do it justice here, but mostly the heat it is coming from the Indian Ocean, much of it via the Agulhas Current flowing around south Africa, "which is augmented by the strengthening of the wind stress curl over the South Atlantic and Indian subtropical gyre." The amount of water "leaking" from the Indian Ocean to the Atlantic Ocean via this route is about 15 times that of all freshwater flowing into the world's oceans.